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This article is cited in 1 scientific paper (total in 1 paper)
Short Notes
An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary
N. S. Goncharov, G. A. Sviridyuk South Ural State University, Chelyabinsk, Russian Federation
Abstract:
The deterministic and stochastic Wentzell systems of Barenblatt–Zheltov–Kochina equations describing moisture filtration in a three-dimensional ball and on its boundary are studied for the first time. In the deterministic case, the unambiguous solvability of the initial problem for the Wentzell system in a specifically constructed Hilbert space is established. In the stochastic case, the Nelson–Glicklich derivative is used and a stochastic solution is constructed, which allows us to predict quantitative changes in the geochemical regime of groundwater under pressureless filtration. For the filtration system under study, the non-classical Wentzell condition was considered, since it is represented by an equation with the Laplace–Beltrami operator defined on the boundary of the domain, understood as a smooth compact Riemannian manifold without an edge, and the external influence is represented by the normal derivative of the function defined in the domain.
Keywords:
Wentzell system, Barenblatt–Zheltov–Kochina equation, Nelson–Glicklich derivative.
Received: 03.08.2023
Citation:
N. S. Goncharov, G. A. Sviridyuk, “An analysis of the Wentzell stochastic system of the equations of moisture filtration in a ball and on its boundary”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 16:4 (2023), 84–92
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https://www.mathnet.ru/eng/vyuru703 https://www.mathnet.ru/eng/vyuru/v16/i4/p84
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